Question

(96 × 10³) × (6.7 x 10²)

O A. 6.432 × 105
O B. 6.432 x 106
O C. 64.32 % 105
D. 64.32 x 106​

Answer 1

Explanation:

remember,

(a×b)×(c×d) = (a×c)×(b×d) = (a×d)×(b×c) = ...

any combination of the 4 numbers or terms.

and

a^b × a^c = a^(b + c)

so, we can easily see the given problem as

(96 × 6.7) × (10³ × 10²) =

= (96 × 6.7) × 10^(3+2) =

= 643.2 × 10⁵

now, exactly this form is not in any of the answer options. so, the teacher tries to trick you.

and I assume that 105 in your question means 10⁵, and 106 means 10⁶, right ?

so, A. and C. have 10⁵ as second term, but they don't have 643.2 as first term. therefore, they are out.

let's see, if one of the 10⁶ answer options can have the same value.

what is the relationship between

10⁵

and

10⁶

?

10⁶ = 10⁵×10¹ = 10⁵×10

so,

x × 10⁶ = x × 10 × 10⁵

x/10 × 10⁶ = x × 10⁵

our x = 643.2

643.2 × 10⁵ = 643.2/10 × 10⁶ = 64.32 × 10⁶

aha !

so,

D. 64.32 × 10⁶ is the correct answer.